VM94

VM94
Heat-generating Plate

Overview

Reference:

F. Kreith, Principles of Heat Transfer, 2nd Printing, International Textbook Co., Scranton, PA, 1959, pg. 42, ex. 2-9.

Analysis Type(s):

Thermal Analysis (ANTYPE = 0)

Element Type(s):

3D Conduction Bar Elements (LINK33)

Convection Link Elements (LINK34)

Input Listing:

vm94.dat

Test Case

A well-mixed fluid is heated by a long iron plate of conductivity k and thickness t. Heat is generated uniformly in the plate at the rate . If the surface convection coefficient is h and the fluid temperature is T_f, determine the temperature at the center of the plate T_c and the heat flow rate to the fluid q_f.

Figure 133: Plate Problem Sketch

Material Properties

Geometric Properties

k = 25 Btu/hr-ft-°F

h = 13.969738 Btu/hr-ft²-°F

t = 1/2 in = 0.041666 ft

= 100,000 Btu/hr-ft³

T_f = 150°F

Analysis Assumptions and Modeling Notes

A 1 ft² area is used for the conduction and convection elements. Only one half of the plate is modeled because of symmetry. Node 6 is given an arbitrary location. POST1 is used to process results from the solution phase.

Results Comparison

	Target	Mechanical APDL	Ratio
q_f,Btu/hr	2083.3	2083.3	1.000
T_c, °F	299.1	300.0	1.003